1 /*
2 * Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10 #include "internal/cryptlib.h"
11 #include "internal/constant_time.h"
12 #include "bn_local.h"
13
14 #include <stdlib.h>
15 #ifdef _WIN32
16 # include <malloc.h>
17 # ifndef alloca
18 # define alloca _alloca
19 # endif
20 #elif defined(__GNUC__)
21 # ifndef alloca
22 # define alloca(s) __builtin_alloca((s))
23 # endif
24 #elif defined(__sun)
25 # include <alloca.h>
26 #endif
27
28 #include "rsaz_exp.h"
29
30 #undef SPARC_T4_MONT
31 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
32 # include "crypto/sparc_arch.h"
33 # define SPARC_T4_MONT
34 #endif
35
36 /* maximum precomputation table size for *variable* sliding windows */
37 #define TABLE_SIZE 32
38
39 /*
40 * Beyond this limit the constant time code is disabled due to
41 * the possible overflow in the computation of powerbufLen in
42 * BN_mod_exp_mont_consttime.
43 * When this limit is exceeded, the computation will be done using
44 * non-constant time code, but it will take very long.
45 */
46 #define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256)
47
48 /* this one works - simple but works */
BN_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)49 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
50 {
51 int i, bits, ret = 0;
52 BIGNUM *v, *rr;
53
54 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
55 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
56 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
57 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
58 return 0;
59 }
60
61 BN_CTX_start(ctx);
62 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
63 v = BN_CTX_get(ctx);
64 if (rr == NULL || v == NULL)
65 goto err;
66
67 if (BN_copy(v, a) == NULL)
68 goto err;
69 bits = BN_num_bits(p);
70
71 if (BN_is_odd(p)) {
72 if (BN_copy(rr, a) == NULL)
73 goto err;
74 } else {
75 if (!BN_one(rr))
76 goto err;
77 }
78
79 for (i = 1; i < bits; i++) {
80 if (!BN_sqr(v, v, ctx))
81 goto err;
82 if (BN_is_bit_set(p, i)) {
83 if (!BN_mul(rr, rr, v, ctx))
84 goto err;
85 }
86 }
87 if (r != rr && BN_copy(r, rr) == NULL)
88 goto err;
89
90 ret = 1;
91 err:
92 BN_CTX_end(ctx);
93 bn_check_top(r);
94 return ret;
95 }
96
BN_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)97 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
98 BN_CTX *ctx)
99 {
100 int ret;
101
102 bn_check_top(a);
103 bn_check_top(p);
104 bn_check_top(m);
105
106 /*-
107 * For even modulus m = 2^k*m_odd, it might make sense to compute
108 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
109 * exponentiation for the odd part), using appropriate exponent
110 * reductions, and combine the results using the CRT.
111 *
112 * For now, we use Montgomery only if the modulus is odd; otherwise,
113 * exponentiation using the reciprocal-based quick remaindering
114 * algorithm is used.
115 *
116 * (Timing obtained with expspeed.c [computations a^p mod m
117 * where a, p, m are of the same length: 256, 512, 1024, 2048,
118 * 4096, 8192 bits], compared to the running time of the
119 * standard algorithm:
120 *
121 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
122 * 55 .. 77 % [UltraSparc processor, but
123 * debug-solaris-sparcv8-gcc conf.]
124 *
125 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
126 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
127 *
128 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
129 * at 2048 and more bits, but at 512 and 1024 bits, it was
130 * slower even than the standard algorithm!
131 *
132 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
133 * should be obtained when the new Montgomery reduction code
134 * has been integrated into OpenSSL.)
135 */
136
137 #define MONT_MUL_MOD
138 #define MONT_EXP_WORD
139 #define RECP_MUL_MOD
140
141 #ifdef MONT_MUL_MOD
142 if (BN_is_odd(m)) {
143 # ifdef MONT_EXP_WORD
144 if (a->top == 1 && !a->neg
145 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
146 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
147 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
148 BN_ULONG A = a->d[0];
149 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
150 } else
151 # endif
152 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
153 } else
154 #endif
155 #ifdef RECP_MUL_MOD
156 {
157 ret = BN_mod_exp_recp(r, a, p, m, ctx);
158 }
159 #else
160 {
161 ret = BN_mod_exp_simple(r, a, p, m, ctx);
162 }
163 #endif
164
165 bn_check_top(r);
166 return ret;
167 }
168
BN_mod_exp_recp(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)169 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
170 const BIGNUM *m, BN_CTX *ctx)
171 {
172 int i, j, bits, ret = 0, wstart, wend, window;
173 int start = 1;
174 BIGNUM *aa;
175 /* Table of variables obtained from 'ctx' */
176 BIGNUM *val[TABLE_SIZE];
177 BN_RECP_CTX recp;
178
179 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
180 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
181 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
182 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
183 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
184 return 0;
185 }
186
187 bits = BN_num_bits(p);
188 if (bits == 0) {
189 /* x**0 mod 1, or x**0 mod -1 is still zero. */
190 if (BN_abs_is_word(m, 1)) {
191 ret = 1;
192 BN_zero(r);
193 } else {
194 ret = BN_one(r);
195 }
196 return ret;
197 }
198
199 BN_RECP_CTX_init(&recp);
200
201 BN_CTX_start(ctx);
202 aa = BN_CTX_get(ctx);
203 val[0] = BN_CTX_get(ctx);
204 if (val[0] == NULL)
205 goto err;
206
207 if (m->neg) {
208 /* ignore sign of 'm' */
209 if (!BN_copy(aa, m))
210 goto err;
211 aa->neg = 0;
212 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
213 goto err;
214 } else {
215 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
216 goto err;
217 }
218
219 if (!BN_nnmod(val[0], a, m, ctx))
220 goto err; /* 1 */
221 if (BN_is_zero(val[0])) {
222 BN_zero(r);
223 ret = 1;
224 goto err;
225 }
226
227 window = BN_window_bits_for_exponent_size(bits);
228 if (window > 1) {
229 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
230 goto err; /* 2 */
231 j = 1 << (window - 1);
232 for (i = 1; i < j; i++) {
233 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
234 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
235 goto err;
236 }
237 }
238
239 start = 1; /* This is used to avoid multiplication etc
240 * when there is only the value '1' in the
241 * buffer. */
242 wstart = bits - 1; /* The top bit of the window */
243 wend = 0; /* The bottom bit of the window */
244
245 if (r == p) {
246 BIGNUM *p_dup = BN_CTX_get(ctx);
247
248 if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
249 goto err;
250 p = p_dup;
251 }
252
253 if (!BN_one(r))
254 goto err;
255
256 for (;;) {
257 int wvalue; /* The 'value' of the window */
258
259 if (BN_is_bit_set(p, wstart) == 0) {
260 if (!start)
261 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
262 goto err;
263 if (wstart == 0)
264 break;
265 wstart--;
266 continue;
267 }
268 /*
269 * We now have wstart on a 'set' bit, we now need to work out how bit
270 * a window to do. To do this we need to scan forward until the last
271 * set bit before the end of the window
272 */
273 wvalue = 1;
274 wend = 0;
275 for (i = 1; i < window; i++) {
276 if (wstart - i < 0)
277 break;
278 if (BN_is_bit_set(p, wstart - i)) {
279 wvalue <<= (i - wend);
280 wvalue |= 1;
281 wend = i;
282 }
283 }
284
285 /* wend is the size of the current window */
286 j = wend + 1;
287 /* add the 'bytes above' */
288 if (!start)
289 for (i = 0; i < j; i++) {
290 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
291 goto err;
292 }
293
294 /* wvalue will be an odd number < 2^window */
295 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
296 goto err;
297
298 /* move the 'window' down further */
299 wstart -= wend + 1;
300 start = 0;
301 if (wstart < 0)
302 break;
303 }
304 ret = 1;
305 err:
306 BN_CTX_end(ctx);
307 BN_RECP_CTX_free(&recp);
308 bn_check_top(r);
309 return ret;
310 }
311
BN_mod_exp_mont(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)312 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
313 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
314 {
315 int i, j, bits, ret = 0, wstart, wend, window;
316 int start = 1;
317 BIGNUM *d, *r;
318 const BIGNUM *aa;
319 /* Table of variables obtained from 'ctx' */
320 BIGNUM *val[TABLE_SIZE];
321 BN_MONT_CTX *mont = NULL;
322
323 bn_check_top(a);
324 bn_check_top(p);
325 bn_check_top(m);
326
327 if (!BN_is_odd(m)) {
328 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
329 return 0;
330 }
331
332 if (m->top <= BN_CONSTTIME_SIZE_LIMIT
333 && (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
334 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
335 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
336 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
337 }
338
339 bits = BN_num_bits(p);
340 if (bits == 0) {
341 /* x**0 mod 1, or x**0 mod -1 is still zero. */
342 if (BN_abs_is_word(m, 1)) {
343 ret = 1;
344 BN_zero(rr);
345 } else {
346 ret = BN_one(rr);
347 }
348 return ret;
349 }
350
351 BN_CTX_start(ctx);
352 d = BN_CTX_get(ctx);
353 r = BN_CTX_get(ctx);
354 val[0] = BN_CTX_get(ctx);
355 if (val[0] == NULL)
356 goto err;
357
358 /*
359 * If this is not done, things will break in the montgomery part
360 */
361
362 if (in_mont != NULL)
363 mont = in_mont;
364 else {
365 if ((mont = BN_MONT_CTX_new()) == NULL)
366 goto err;
367 if (!BN_MONT_CTX_set(mont, m, ctx))
368 goto err;
369 }
370
371 if (a->neg || BN_ucmp(a, m) >= 0) {
372 if (!BN_nnmod(val[0], a, m, ctx))
373 goto err;
374 aa = val[0];
375 } else
376 aa = a;
377 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
378 goto err; /* 1 */
379
380 window = BN_window_bits_for_exponent_size(bits);
381 if (window > 1) {
382 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
383 goto err; /* 2 */
384 j = 1 << (window - 1);
385 for (i = 1; i < j; i++) {
386 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
387 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
388 goto err;
389 }
390 }
391
392 start = 1; /* This is used to avoid multiplication etc
393 * when there is only the value '1' in the
394 * buffer. */
395 wstart = bits - 1; /* The top bit of the window */
396 wend = 0; /* The bottom bit of the window */
397
398 #if 1 /* by Shay Gueron's suggestion */
399 j = m->top; /* borrow j */
400 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
401 if (bn_wexpand(r, j) == NULL)
402 goto err;
403 /* 2^(top*BN_BITS2) - m */
404 r->d[0] = (0 - m->d[0]) & BN_MASK2;
405 for (i = 1; i < j; i++)
406 r->d[i] = (~m->d[i]) & BN_MASK2;
407 r->top = j;
408 r->flags |= BN_FLG_FIXED_TOP;
409 } else
410 #endif
411 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
412 goto err;
413 for (;;) {
414 int wvalue; /* The 'value' of the window */
415
416 if (BN_is_bit_set(p, wstart) == 0) {
417 if (!start) {
418 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
419 goto err;
420 }
421 if (wstart == 0)
422 break;
423 wstart--;
424 continue;
425 }
426 /*
427 * We now have wstart on a 'set' bit, we now need to work out how bit
428 * a window to do. To do this we need to scan forward until the last
429 * set bit before the end of the window
430 */
431 wvalue = 1;
432 wend = 0;
433 for (i = 1; i < window; i++) {
434 if (wstart - i < 0)
435 break;
436 if (BN_is_bit_set(p, wstart - i)) {
437 wvalue <<= (i - wend);
438 wvalue |= 1;
439 wend = i;
440 }
441 }
442
443 /* wend is the size of the current window */
444 j = wend + 1;
445 /* add the 'bytes above' */
446 if (!start)
447 for (i = 0; i < j; i++) {
448 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
449 goto err;
450 }
451
452 /* wvalue will be an odd number < 2^window */
453 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
454 goto err;
455
456 /* move the 'window' down further */
457 wstart -= wend + 1;
458 start = 0;
459 if (wstart < 0)
460 break;
461 }
462 /*
463 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
464 * removes padding [if any] and makes return value suitable for public
465 * API consumer.
466 */
467 #if defined(SPARC_T4_MONT)
468 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
469 j = mont->N.top; /* borrow j */
470 val[0]->d[0] = 1; /* borrow val[0] */
471 for (i = 1; i < j; i++)
472 val[0]->d[i] = 0;
473 val[0]->top = j;
474 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
475 goto err;
476 } else
477 #endif
478 if (!BN_from_montgomery(rr, r, mont, ctx))
479 goto err;
480 ret = 1;
481 err:
482 if (in_mont == NULL)
483 BN_MONT_CTX_free(mont);
484 BN_CTX_end(ctx);
485 bn_check_top(rr);
486 return ret;
487 }
488
bn_get_bits(const BIGNUM * a,int bitpos)489 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
490 {
491 BN_ULONG ret = 0;
492 int wordpos;
493
494 wordpos = bitpos / BN_BITS2;
495 bitpos %= BN_BITS2;
496 if (wordpos >= 0 && wordpos < a->top) {
497 ret = a->d[wordpos] & BN_MASK2;
498 if (bitpos) {
499 ret >>= bitpos;
500 if (++wordpos < a->top)
501 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
502 }
503 }
504
505 return ret & BN_MASK2;
506 }
507
508 /*
509 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
510 * layout so that accessing any of these table values shows the same access
511 * pattern as far as cache lines are concerned. The following functions are
512 * used to transfer a BIGNUM from/to that table.
513 */
514
MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM * b,int top,unsigned char * buf,int idx,int window)515 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
516 unsigned char *buf, int idx,
517 int window)
518 {
519 int i, j;
520 int width = 1 << window;
521 BN_ULONG *table = (BN_ULONG *)buf;
522
523 if (top > b->top)
524 top = b->top; /* this works because 'buf' is explicitly
525 * zeroed */
526 for (i = 0, j = idx; i < top; i++, j += width) {
527 table[j] = b->d[i];
528 }
529
530 return 1;
531 }
532
MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM * b,int top,unsigned char * buf,int idx,int window)533 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
534 unsigned char *buf, int idx,
535 int window)
536 {
537 int i, j;
538 int width = 1 << window;
539 /*
540 * We declare table 'volatile' in order to discourage compiler
541 * from reordering loads from the table. Concern is that if
542 * reordered in specific manner loads might give away the
543 * information we are trying to conceal. Some would argue that
544 * compiler can reorder them anyway, but it can as well be
545 * argued that doing so would be violation of standard...
546 */
547 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
548
549 if (bn_wexpand(b, top) == NULL)
550 return 0;
551
552 if (window <= 3) {
553 for (i = 0; i < top; i++, table += width) {
554 BN_ULONG acc = 0;
555
556 for (j = 0; j < width; j++) {
557 acc |= table[j] &
558 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
559 }
560
561 b->d[i] = acc;
562 }
563 } else {
564 int xstride = 1 << (window - 2);
565 BN_ULONG y0, y1, y2, y3;
566
567 i = idx >> (window - 2); /* equivalent of idx / xstride */
568 idx &= xstride - 1; /* equivalent of idx % xstride */
569
570 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
571 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
572 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
573 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
574
575 for (i = 0; i < top; i++, table += width) {
576 BN_ULONG acc = 0;
577
578 for (j = 0; j < xstride; j++) {
579 acc |= ( (table[j + 0 * xstride] & y0) |
580 (table[j + 1 * xstride] & y1) |
581 (table[j + 2 * xstride] & y2) |
582 (table[j + 3 * xstride] & y3) )
583 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
584 }
585
586 b->d[i] = acc;
587 }
588 }
589
590 b->top = top;
591 b->flags |= BN_FLG_FIXED_TOP;
592 return 1;
593 }
594
595 /*
596 * Given a pointer value, compute the next address that is a cache line
597 * multiple.
598 */
599 #define MOD_EXP_CTIME_ALIGN(x_) \
600 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
601
602 /*
603 * This variant of BN_mod_exp_mont() uses fixed windows and the special
604 * precomputation memory layout to limit data-dependency to a minimum to
605 * protect secret exponents (cf. the hyper-threading timing attacks pointed
606 * out by Colin Percival,
607 * http://www.daemonology.net/hyperthreading-considered-harmful/)
608 */
BN_mod_exp_mont_consttime(BIGNUM * rr,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)609 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
610 const BIGNUM *m, BN_CTX *ctx,
611 BN_MONT_CTX *in_mont)
612 {
613 int i, bits, ret = 0, window, wvalue, wmask, window0;
614 int top;
615 BN_MONT_CTX *mont = NULL;
616
617 int numPowers;
618 unsigned char *powerbufFree = NULL;
619 int powerbufLen = 0;
620 unsigned char *powerbuf = NULL;
621 BIGNUM tmp, am;
622 #if defined(SPARC_T4_MONT)
623 unsigned int t4 = 0;
624 #endif
625
626 bn_check_top(a);
627 bn_check_top(p);
628 bn_check_top(m);
629
630 if (!BN_is_odd(m)) {
631 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
632 return 0;
633 }
634
635 top = m->top;
636
637 if (top > BN_CONSTTIME_SIZE_LIMIT) {
638 /* Prevent overflowing the powerbufLen computation below */
639 return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
640 }
641
642 /*
643 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
644 * whether the top bits are zero.
645 */
646 bits = p->top * BN_BITS2;
647 if (bits == 0) {
648 /* x**0 mod 1, or x**0 mod -1 is still zero. */
649 if (BN_abs_is_word(m, 1)) {
650 ret = 1;
651 BN_zero(rr);
652 } else {
653 ret = BN_one(rr);
654 }
655 return ret;
656 }
657
658 BN_CTX_start(ctx);
659
660 /*
661 * Allocate a montgomery context if it was not supplied by the caller. If
662 * this is not done, things will break in the montgomery part.
663 */
664 if (in_mont != NULL)
665 mont = in_mont;
666 else {
667 if ((mont = BN_MONT_CTX_new()) == NULL)
668 goto err;
669 if (!BN_MONT_CTX_set(mont, m, ctx))
670 goto err;
671 }
672
673 if (a->neg || BN_ucmp(a, m) >= 0) {
674 BIGNUM *reduced = BN_CTX_get(ctx);
675 if (reduced == NULL
676 || !BN_nnmod(reduced, a, m, ctx)) {
677 goto err;
678 }
679 a = reduced;
680 }
681
682 #ifdef RSAZ_ENABLED
683 /*
684 * If the size of the operands allow it, perform the optimized
685 * RSAZ exponentiation. For further information see
686 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
687 */
688 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
689 && rsaz_avx2_eligible()) {
690 if (NULL == bn_wexpand(rr, 16))
691 goto err;
692 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
693 mont->n0[0]);
694 rr->top = 16;
695 rr->neg = 0;
696 bn_correct_top(rr);
697 ret = 1;
698 goto err;
699 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
700 if (NULL == bn_wexpand(rr, 8))
701 goto err;
702 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
703 rr->top = 8;
704 rr->neg = 0;
705 bn_correct_top(rr);
706 ret = 1;
707 goto err;
708 }
709 #endif
710
711 /* Get the window size to use with size of p. */
712 window = BN_window_bits_for_ctime_exponent_size(bits);
713 #if defined(SPARC_T4_MONT)
714 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
715 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
716 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
717 window = 5;
718 else
719 #endif
720 #if defined(OPENSSL_BN_ASM_MONT5)
721 if (window >= 5 && top <= BN_SOFT_LIMIT) {
722 window = 5; /* ~5% improvement for RSA2048 sign, and even
723 * for RSA4096 */
724 /* reserve space for mont->N.d[] copy */
725 powerbufLen += top * sizeof(mont->N.d[0]);
726 }
727 #endif
728 (void)0;
729
730 /*
731 * Allocate a buffer large enough to hold all of the pre-computed powers
732 * of am, am itself and tmp.
733 */
734 numPowers = 1 << window;
735 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
736 ((2 * top) >
737 numPowers ? (2 * top) : numPowers));
738 #ifdef alloca
739 if (powerbufLen < 3072)
740 powerbufFree =
741 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
742 else
743 #endif
744 if ((powerbufFree =
745 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
746 == NULL)
747 goto err;
748
749 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
750 memset(powerbuf, 0, powerbufLen);
751
752 #ifdef alloca
753 if (powerbufLen < 3072)
754 powerbufFree = NULL;
755 #endif
756
757 /* lay down tmp and am right after powers table */
758 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
759 am.d = tmp.d + top;
760 tmp.top = am.top = 0;
761 tmp.dmax = am.dmax = top;
762 tmp.neg = am.neg = 0;
763 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
764
765 /* prepare a^0 in Montgomery domain */
766 #if 1 /* by Shay Gueron's suggestion */
767 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
768 /* 2^(top*BN_BITS2) - m */
769 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
770 for (i = 1; i < top; i++)
771 tmp.d[i] = (~m->d[i]) & BN_MASK2;
772 tmp.top = top;
773 } else
774 #endif
775 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
776 goto err;
777
778 /* prepare a^1 in Montgomery domain */
779 if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
780 goto err;
781
782 if (top > BN_SOFT_LIMIT)
783 goto fallback;
784
785 #if defined(SPARC_T4_MONT)
786 if (t4) {
787 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
788 const BN_ULONG *n0, const void *table,
789 int power, int bits);
790 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
791 const BN_ULONG *n0, const void *table,
792 int power, int bits);
793 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
794 const BN_ULONG *n0, const void *table,
795 int power, int bits);
796 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
797 const BN_ULONG *n0, const void *table,
798 int power, int bits);
799 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
800 const BN_ULONG *n0, const void *table,
801 int power, int bits);
802 static const bn_pwr5_mont_f pwr5_funcs[4] = {
803 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
804 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
805 };
806 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
807
808 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
809 const void *bp, const BN_ULONG *np,
810 const BN_ULONG *n0);
811 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
812 const BN_ULONG *np, const BN_ULONG *n0);
813 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
814 const void *bp, const BN_ULONG *np,
815 const BN_ULONG *n0);
816 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
817 const void *bp, const BN_ULONG *np,
818 const BN_ULONG *n0);
819 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
820 const void *bp, const BN_ULONG *np,
821 const BN_ULONG *n0);
822 static const bn_mul_mont_f mul_funcs[4] = {
823 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
824 bn_mul_mont_t4_24, bn_mul_mont_t4_32
825 };
826 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
827
828 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
829 const void *bp, const BN_ULONG *np,
830 const BN_ULONG *n0, int num);
831 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
832 const void *bp, const BN_ULONG *np,
833 const BN_ULONG *n0, int num);
834 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
835 const void *table, const BN_ULONG *np,
836 const BN_ULONG *n0, int num, int power);
837 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
838 void *table, size_t power);
839 void bn_gather5_t4(BN_ULONG *out, size_t num,
840 void *table, size_t power);
841 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
842
843 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
844 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
845 * than 32 */
846
847 /*
848 * BN_to_montgomery can contaminate words above .top [in
849 * BN_DEBUG build...
850 */
851 for (i = am.top; i < top; i++)
852 am.d[i] = 0;
853 for (i = tmp.top; i < top; i++)
854 tmp.d[i] = 0;
855
856 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
857 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
858 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
859 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
860 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
861 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
862
863 for (i = 3; i < 32; i++) {
864 /* Calculate a^i = a^(i-1) * a */
865 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
866 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
867 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
868 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
869 }
870
871 /* switch to 64-bit domain */
872 np = alloca(top * sizeof(BN_ULONG));
873 top /= 2;
874 bn_flip_t4(np, mont->N.d, top);
875
876 /*
877 * The exponent may not have a whole number of fixed-size windows.
878 * To simplify the main loop, the initial window has between 1 and
879 * full-window-size bits such that what remains is always a whole
880 * number of windows
881 */
882 window0 = (bits - 1) % 5 + 1;
883 wmask = (1 << window0) - 1;
884 bits -= window0;
885 wvalue = bn_get_bits(p, bits) & wmask;
886 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
887
888 /*
889 * Scan the exponent one window at a time starting from the most
890 * significant bits.
891 */
892 while (bits > 0) {
893 if (bits < stride)
894 stride = bits;
895 bits -= stride;
896 wvalue = bn_get_bits(p, bits);
897
898 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
899 continue;
900 /* retry once and fall back */
901 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
902 continue;
903
904 bits += stride - 5;
905 wvalue >>= stride - 5;
906 wvalue &= 31;
907 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
908 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
909 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
910 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
911 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
912 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
913 wvalue);
914 }
915
916 bn_flip_t4(tmp.d, tmp.d, top);
917 top *= 2;
918 /* back to 32-bit domain */
919 tmp.top = top;
920 bn_correct_top(&tmp);
921 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
922 } else
923 #endif
924 #if defined(OPENSSL_BN_ASM_MONT5)
925 if (window == 5 && top > 1) {
926 /*
927 * This optimization uses ideas from https://eprint.iacr.org/2011/239,
928 * specifically optimization of cache-timing attack countermeasures,
929 * pre-computation optimization, and Almost Montgomery Multiplication.
930 *
931 * The paper discusses a 4-bit window to optimize 512-bit modular
932 * exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
933 * important.
934 *
935 * |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
936 * reduction variant, so the values here may not be fully reduced.
937 * They are bounded by R (i.e. they fit in |top| words), not |m|.
938 * Additionally, we pass these "almost" reduced inputs into
939 * |bn_mul_mont|, which implements the normal reduction variant.
940 * Given those inputs, |bn_mul_mont| may not give reduced
941 * output, but it will still produce "almost" reduced output.
942 */
943 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
944 const void *table, const BN_ULONG *np,
945 const BN_ULONG *n0, int num, int power);
946 void bn_scatter5(const BN_ULONG *inp, size_t num,
947 void *table, size_t power);
948 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
949 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
950 const void *table, const BN_ULONG *np,
951 const BN_ULONG *n0, int num, int power);
952 int bn_get_bits5(const BN_ULONG *ap, int off);
953
954 BN_ULONG *n0 = mont->n0, *np;
955
956 /*
957 * BN_to_montgomery can contaminate words above .top [in
958 * BN_DEBUG build...
959 */
960 for (i = am.top; i < top; i++)
961 am.d[i] = 0;
962 for (i = tmp.top; i < top; i++)
963 tmp.d[i] = 0;
964
965 /*
966 * copy mont->N.d[] to improve cache locality
967 */
968 for (np = am.d + top, i = 0; i < top; i++)
969 np[i] = mont->N.d[i];
970
971 bn_scatter5(tmp.d, top, powerbuf, 0);
972 bn_scatter5(am.d, am.top, powerbuf, 1);
973 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
974 bn_scatter5(tmp.d, top, powerbuf, 2);
975
976 # if 0
977 for (i = 3; i < 32; i++) {
978 /* Calculate a^i = a^(i-1) * a */
979 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
980 bn_scatter5(tmp.d, top, powerbuf, i);
981 }
982 # else
983 /* same as above, but uses squaring for 1/2 of operations */
984 for (i = 4; i < 32; i *= 2) {
985 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
986 bn_scatter5(tmp.d, top, powerbuf, i);
987 }
988 for (i = 3; i < 8; i += 2) {
989 int j;
990 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
991 bn_scatter5(tmp.d, top, powerbuf, i);
992 for (j = 2 * i; j < 32; j *= 2) {
993 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
994 bn_scatter5(tmp.d, top, powerbuf, j);
995 }
996 }
997 for (; i < 16; i += 2) {
998 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
999 bn_scatter5(tmp.d, top, powerbuf, i);
1000 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1001 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1002 }
1003 for (; i < 32; i += 2) {
1004 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1005 bn_scatter5(tmp.d, top, powerbuf, i);
1006 }
1007 # endif
1008 /*
1009 * The exponent may not have a whole number of fixed-size windows.
1010 * To simplify the main loop, the initial window has between 1 and
1011 * full-window-size bits such that what remains is always a whole
1012 * number of windows
1013 */
1014 window0 = (bits - 1) % 5 + 1;
1015 wmask = (1 << window0) - 1;
1016 bits -= window0;
1017 wvalue = bn_get_bits(p, bits) & wmask;
1018 bn_gather5(tmp.d, top, powerbuf, wvalue);
1019
1020 /*
1021 * Scan the exponent one window at a time starting from the most
1022 * significant bits.
1023 */
1024 if (top & 7) {
1025 while (bits > 0) {
1026 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1027 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1028 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1029 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1030 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1031 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1032 bn_get_bits5(p->d, bits -= 5));
1033 }
1034 } else {
1035 while (bits > 0) {
1036 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1037 bn_get_bits5(p->d, bits -= 5));
1038 }
1039 }
1040
1041 tmp.top = top;
1042 /*
1043 * The result is now in |tmp| in Montgomery form, but it may not be
1044 * fully reduced. This is within bounds for |BN_from_montgomery|
1045 * (tmp < R <= m*R) so it will, when converting from Montgomery form,
1046 * produce a fully reduced result.
1047 *
1048 * This differs from Figure 2 of the paper, which uses AMM(h, 1) to
1049 * convert from Montgomery form with unreduced output, followed by an
1050 * extra reduction step. In the paper's terminology, we replace
1051 * steps 9 and 10 with MM(h, 1).
1052 */
1053 } else
1054 #endif
1055 {
1056 fallback:
1057 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1058 goto err;
1059 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1060 goto err;
1061
1062 /*
1063 * If the window size is greater than 1, then calculate
1064 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1065 * powers could instead be computed as (a^(i/2))^2 to use the slight
1066 * performance advantage of sqr over mul).
1067 */
1068 if (window > 1) {
1069 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1070 goto err;
1071 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1072 window))
1073 goto err;
1074 for (i = 3; i < numPowers; i++) {
1075 /* Calculate a^i = a^(i-1) * a */
1076 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1077 goto err;
1078 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1079 window))
1080 goto err;
1081 }
1082 }
1083
1084 /*
1085 * The exponent may not have a whole number of fixed-size windows.
1086 * To simplify the main loop, the initial window has between 1 and
1087 * full-window-size bits such that what remains is always a whole
1088 * number of windows
1089 */
1090 window0 = (bits - 1) % window + 1;
1091 wmask = (1 << window0) - 1;
1092 bits -= window0;
1093 wvalue = bn_get_bits(p, bits) & wmask;
1094 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1095 window))
1096 goto err;
1097
1098 wmask = (1 << window) - 1;
1099 /*
1100 * Scan the exponent one window at a time starting from the most
1101 * significant bits.
1102 */
1103 while (bits > 0) {
1104
1105 /* Square the result window-size times */
1106 for (i = 0; i < window; i++)
1107 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1108 goto err;
1109
1110 /*
1111 * Get a window's worth of bits from the exponent
1112 * This avoids calling BN_is_bit_set for each bit, which
1113 * is not only slower but also makes each bit vulnerable to
1114 * EM (and likely other) side-channel attacks like One&Done
1115 * (for details see "One&Done: A Single-Decryption EM-Based
1116 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1117 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1118 * M. Prvulovic, in USENIX Security'18)
1119 */
1120 bits -= window;
1121 wvalue = bn_get_bits(p, bits) & wmask;
1122 /*
1123 * Fetch the appropriate pre-computed value from the pre-buf
1124 */
1125 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1126 window))
1127 goto err;
1128
1129 /* Multiply the result into the intermediate result */
1130 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1131 goto err;
1132 }
1133 }
1134
1135 /*
1136 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1137 * removes padding [if any] and makes return value suitable for public
1138 * API consumer.
1139 */
1140 #if defined(SPARC_T4_MONT)
1141 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1142 am.d[0] = 1; /* borrow am */
1143 for (i = 1; i < top; i++)
1144 am.d[i] = 0;
1145 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1146 goto err;
1147 } else
1148 #endif
1149 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1150 goto err;
1151 ret = 1;
1152 err:
1153 if (in_mont == NULL)
1154 BN_MONT_CTX_free(mont);
1155 if (powerbuf != NULL) {
1156 OPENSSL_cleanse(powerbuf, powerbufLen);
1157 OPENSSL_free(powerbufFree);
1158 }
1159 BN_CTX_end(ctx);
1160 return ret;
1161 }
1162
BN_mod_exp_mont_word(BIGNUM * rr,BN_ULONG a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)1163 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1164 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1165 {
1166 BN_MONT_CTX *mont = NULL;
1167 int b, bits, ret = 0;
1168 int r_is_one;
1169 BN_ULONG w, next_w;
1170 BIGNUM *r, *t;
1171 BIGNUM *swap_tmp;
1172 #define BN_MOD_MUL_WORD(r, w, m) \
1173 (BN_mul_word(r, (w)) && \
1174 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1175 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1176 /*
1177 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1178 * probably more overhead than always using BN_mod (which uses BN_copy if
1179 * a similar test returns true).
1180 */
1181 /*
1182 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1183 * never negative (the result of BN_mod does not depend on the sign of
1184 * the modulus).
1185 */
1186 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1187 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1188
1189 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1190 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1191 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1192 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1193 return 0;
1194 }
1195
1196 bn_check_top(p);
1197 bn_check_top(m);
1198
1199 if (!BN_is_odd(m)) {
1200 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
1201 return 0;
1202 }
1203 if (m->top == 1)
1204 a %= m->d[0]; /* make sure that 'a' is reduced */
1205
1206 bits = BN_num_bits(p);
1207 if (bits == 0) {
1208 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1209 if (BN_abs_is_word(m, 1)) {
1210 ret = 1;
1211 BN_zero(rr);
1212 } else {
1213 ret = BN_one(rr);
1214 }
1215 return ret;
1216 }
1217 if (a == 0) {
1218 BN_zero(rr);
1219 ret = 1;
1220 return ret;
1221 }
1222
1223 BN_CTX_start(ctx);
1224 r = BN_CTX_get(ctx);
1225 t = BN_CTX_get(ctx);
1226 if (t == NULL)
1227 goto err;
1228
1229 if (in_mont != NULL)
1230 mont = in_mont;
1231 else {
1232 if ((mont = BN_MONT_CTX_new()) == NULL)
1233 goto err;
1234 if (!BN_MONT_CTX_set(mont, m, ctx))
1235 goto err;
1236 }
1237
1238 r_is_one = 1; /* except for Montgomery factor */
1239
1240 /* bits-1 >= 0 */
1241
1242 /* The result is accumulated in the product r*w. */
1243 w = a; /* bit 'bits-1' of 'p' is always set */
1244 for (b = bits - 2; b >= 0; b--) {
1245 /* First, square r*w. */
1246 next_w = w * w;
1247 if ((next_w / w) != w) { /* overflow */
1248 if (r_is_one) {
1249 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1250 goto err;
1251 r_is_one = 0;
1252 } else {
1253 if (!BN_MOD_MUL_WORD(r, w, m))
1254 goto err;
1255 }
1256 next_w = 1;
1257 }
1258 w = next_w;
1259 if (!r_is_one) {
1260 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1261 goto err;
1262 }
1263
1264 /* Second, multiply r*w by 'a' if exponent bit is set. */
1265 if (BN_is_bit_set(p, b)) {
1266 next_w = w * a;
1267 if ((next_w / a) != w) { /* overflow */
1268 if (r_is_one) {
1269 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1270 goto err;
1271 r_is_one = 0;
1272 } else {
1273 if (!BN_MOD_MUL_WORD(r, w, m))
1274 goto err;
1275 }
1276 next_w = a;
1277 }
1278 w = next_w;
1279 }
1280 }
1281
1282 /* Finally, set r:=r*w. */
1283 if (w != 1) {
1284 if (r_is_one) {
1285 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1286 goto err;
1287 r_is_one = 0;
1288 } else {
1289 if (!BN_MOD_MUL_WORD(r, w, m))
1290 goto err;
1291 }
1292 }
1293
1294 if (r_is_one) { /* can happen only if a == 1 */
1295 if (!BN_one(rr))
1296 goto err;
1297 } else {
1298 if (!BN_from_montgomery(rr, r, mont, ctx))
1299 goto err;
1300 }
1301 ret = 1;
1302 err:
1303 if (in_mont == NULL)
1304 BN_MONT_CTX_free(mont);
1305 BN_CTX_end(ctx);
1306 bn_check_top(rr);
1307 return ret;
1308 }
1309
1310 /* The old fallback, simple version :-) */
BN_mod_exp_simple(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,const BIGNUM * m,BN_CTX * ctx)1311 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1312 const BIGNUM *m, BN_CTX *ctx)
1313 {
1314 int i, j, bits, ret = 0, wstart, wend, window;
1315 int start = 1;
1316 BIGNUM *d;
1317 /* Table of variables obtained from 'ctx' */
1318 BIGNUM *val[TABLE_SIZE];
1319
1320 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1321 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1322 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1323 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1324 ERR_raise(ERR_LIB_BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1325 return 0;
1326 }
1327
1328 if (r == m) {
1329 ERR_raise(ERR_LIB_BN, ERR_R_PASSED_INVALID_ARGUMENT);
1330 return 0;
1331 }
1332
1333 bits = BN_num_bits(p);
1334 if (bits == 0) {
1335 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1336 if (BN_abs_is_word(m, 1)) {
1337 ret = 1;
1338 BN_zero(r);
1339 } else {
1340 ret = BN_one(r);
1341 }
1342 return ret;
1343 }
1344
1345 BN_CTX_start(ctx);
1346 d = BN_CTX_get(ctx);
1347 val[0] = BN_CTX_get(ctx);
1348 if (val[0] == NULL)
1349 goto err;
1350
1351 if (!BN_nnmod(val[0], a, m, ctx))
1352 goto err; /* 1 */
1353 if (BN_is_zero(val[0])) {
1354 BN_zero(r);
1355 ret = 1;
1356 goto err;
1357 }
1358
1359 window = BN_window_bits_for_exponent_size(bits);
1360 if (window > 1) {
1361 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1362 goto err; /* 2 */
1363 j = 1 << (window - 1);
1364 for (i = 1; i < j; i++) {
1365 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1366 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1367 goto err;
1368 }
1369 }
1370
1371 start = 1; /* This is used to avoid multiplication etc
1372 * when there is only the value '1' in the
1373 * buffer. */
1374 wstart = bits - 1; /* The top bit of the window */
1375 wend = 0; /* The bottom bit of the window */
1376
1377 if (r == p) {
1378 BIGNUM *p_dup = BN_CTX_get(ctx);
1379
1380 if (p_dup == NULL || BN_copy(p_dup, p) == NULL)
1381 goto err;
1382 p = p_dup;
1383 }
1384
1385 if (!BN_one(r))
1386 goto err;
1387
1388 for (;;) {
1389 int wvalue; /* The 'value' of the window */
1390
1391 if (BN_is_bit_set(p, wstart) == 0) {
1392 if (!start)
1393 if (!BN_mod_mul(r, r, r, m, ctx))
1394 goto err;
1395 if (wstart == 0)
1396 break;
1397 wstart--;
1398 continue;
1399 }
1400 /*
1401 * We now have wstart on a 'set' bit, we now need to work out how bit
1402 * a window to do. To do this we need to scan forward until the last
1403 * set bit before the end of the window
1404 */
1405 wvalue = 1;
1406 wend = 0;
1407 for (i = 1; i < window; i++) {
1408 if (wstart - i < 0)
1409 break;
1410 if (BN_is_bit_set(p, wstart - i)) {
1411 wvalue <<= (i - wend);
1412 wvalue |= 1;
1413 wend = i;
1414 }
1415 }
1416
1417 /* wend is the size of the current window */
1418 j = wend + 1;
1419 /* add the 'bytes above' */
1420 if (!start)
1421 for (i = 0; i < j; i++) {
1422 if (!BN_mod_mul(r, r, r, m, ctx))
1423 goto err;
1424 }
1425
1426 /* wvalue will be an odd number < 2^window */
1427 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1428 goto err;
1429
1430 /* move the 'window' down further */
1431 wstart -= wend + 1;
1432 start = 0;
1433 if (wstart < 0)
1434 break;
1435 }
1436 ret = 1;
1437 err:
1438 BN_CTX_end(ctx);
1439 bn_check_top(r);
1440 return ret;
1441 }
1442
1443 /*
1444 * This is a variant of modular exponentiation optimization that does
1445 * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1446 * in 52-bit binary redundant representation.
1447 * If such instructions are not available, or input data size is not supported,
1448 * it falls back to two BN_mod_exp_mont_consttime() calls.
1449 */
BN_mod_exp_mont_consttime_x2(BIGNUM * rr1,const BIGNUM * a1,const BIGNUM * p1,const BIGNUM * m1,BN_MONT_CTX * in_mont1,BIGNUM * rr2,const BIGNUM * a2,const BIGNUM * p2,const BIGNUM * m2,BN_MONT_CTX * in_mont2,BN_CTX * ctx)1450 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, const BIGNUM *p1,
1451 const BIGNUM *m1, BN_MONT_CTX *in_mont1,
1452 BIGNUM *rr2, const BIGNUM *a2, const BIGNUM *p2,
1453 const BIGNUM *m2, BN_MONT_CTX *in_mont2,
1454 BN_CTX *ctx)
1455 {
1456 int ret = 0;
1457
1458 #ifdef RSAZ_ENABLED
1459 BN_MONT_CTX *mont1 = NULL;
1460 BN_MONT_CTX *mont2 = NULL;
1461
1462 if (ossl_rsaz_avx512ifma_eligible() &&
1463 (((a1->top == 16) && (p1->top == 16) && (BN_num_bits(m1) == 1024) &&
1464 (a2->top == 16) && (p2->top == 16) && (BN_num_bits(m2) == 1024)) ||
1465 ((a1->top == 24) && (p1->top == 24) && (BN_num_bits(m1) == 1536) &&
1466 (a2->top == 24) && (p2->top == 24) && (BN_num_bits(m2) == 1536)) ||
1467 ((a1->top == 32) && (p1->top == 32) && (BN_num_bits(m1) == 2048) &&
1468 (a2->top == 32) && (p2->top == 32) && (BN_num_bits(m2) == 2048)))) {
1469
1470 int topn = a1->top;
1471 /* Modulus bits of |m1| and |m2| are equal */
1472 int mod_bits = BN_num_bits(m1);
1473
1474 if (bn_wexpand(rr1, topn) == NULL)
1475 goto err;
1476 if (bn_wexpand(rr2, topn) == NULL)
1477 goto err;
1478
1479 /* Ensure that montgomery contexts are initialized */
1480 if (in_mont1 != NULL) {
1481 mont1 = in_mont1;
1482 } else {
1483 if ((mont1 = BN_MONT_CTX_new()) == NULL)
1484 goto err;
1485 if (!BN_MONT_CTX_set(mont1, m1, ctx))
1486 goto err;
1487 }
1488 if (in_mont2 != NULL) {
1489 mont2 = in_mont2;
1490 } else {
1491 if ((mont2 = BN_MONT_CTX_new()) == NULL)
1492 goto err;
1493 if (!BN_MONT_CTX_set(mont2, m2, ctx))
1494 goto err;
1495 }
1496
1497 ret = ossl_rsaz_mod_exp_avx512_x2(rr1->d, a1->d, p1->d, m1->d,
1498 mont1->RR.d, mont1->n0[0],
1499 rr2->d, a2->d, p2->d, m2->d,
1500 mont2->RR.d, mont2->n0[0],
1501 mod_bits);
1502
1503 rr1->top = topn;
1504 rr1->neg = 0;
1505 bn_correct_top(rr1);
1506 bn_check_top(rr1);
1507
1508 rr2->top = topn;
1509 rr2->neg = 0;
1510 bn_correct_top(rr2);
1511 bn_check_top(rr2);
1512
1513 goto err;
1514 }
1515 #endif
1516
1517 /* rr1 = a1^p1 mod m1 */
1518 ret = BN_mod_exp_mont_consttime(rr1, a1, p1, m1, ctx, in_mont1);
1519 /* rr2 = a2^p2 mod m2 */
1520 ret &= BN_mod_exp_mont_consttime(rr2, a2, p2, m2, ctx, in_mont2);
1521
1522 #ifdef RSAZ_ENABLED
1523 err:
1524 if (in_mont2 == NULL)
1525 BN_MONT_CTX_free(mont2);
1526 if (in_mont1 == NULL)
1527 BN_MONT_CTX_free(mont1);
1528 #endif
1529
1530 return ret;
1531 }
1532
